Sports
Match Outcome Distribution Calculator
Inspect the ranked exact-score distribution, probability concentration, clean sheets, score entropy, and displayed grid coverage from two Poisson goal rates.
SCORELINE SHAPE
Measure how probability is distributed across exact scores
This calculator is designed for distribution questions: which scorelines dominate, how concentrated the model is, how much probability fits within a chosen display square, and how likely either side is to keep a clean sheet.
CURRENT DECISION RECORD
Ranked exact-score distribution
Every row is generated from the current inputs and reused by Copy, TXT, and the page-specific PDF.
| Rank | Exact score | Probability (%) | Cumulative top-score mass (%) | Total goals |
|---|
CURRENT CALCULATION PROCESS
Formula, substitution, intermediate values, and reconciliation
P(h,a) = Poisson(h; lambdaHome) x Poisson(a; lambdaAway); entropy = -sum(P(h,a) x log2(P(h,a)))
Waiting for valid inputs.
USE STEPS
Five steps for reading scoreline shape
- Enter home and away goal rates from a consistent pre-match model.
- Select a displayed goal cap large enough for the scoring environment.
- Inspect the modal score and cumulative mass of the top ranked cells.
- Compare clean-sheet probabilities and entropy with tactical expectations.
- Preserve display coverage and omitted-tail evidence with any published interpretation.
FOUNDATIONS
Five distribution concepts
Joint score cell
One home count and one away count form a mutually exclusive exact-match outcome.
Ranked mass
Sorting cells by probability shows how quickly the most plausible scores accumulate coverage.
Clean-sheet marginal
A team's clean-sheet probability sums every score cell where the opponent has zero goals.
Score entropy
Entropy rises when probability is spread more evenly across many scorelines.
Display coverage
The selected square is a presentation boundary; its coverage proves how much model mass remains outside it.
DEEP ANALYSIS
Three distribution questions beyond the mode
Mode is not forecast certainty
The top score is often far below 20% probability. Communicating only that score discards most of the distribution and creates false confidence.
Entropy as concentration context
Two matches can share a 1-0 mode while one has much more dispersed alternatives. Entropy and cumulative top-cell mass distinguish those profiles.
Grid adequacy
A 0-3 display may be adequate for low rates but hide meaningful mass in a high-scoring match. Increase the cap until coverage meets the reporting standard.
DECISION CASES
Two score distributions with different stories
Low-event defensive match
Rates of 0.75 and 0.65 concentrate mass in 0-0, 1-0, 0-1, and 1-1. The mode is informative, entropy is relatively low, and a compact display covers nearly all probability.
Open high-rate derby
Rates of 2.25 and 1.85 spread mass across many scorelines. No exact score dominates, entropy rises, and the analyst increases the display cap before sharing a ranked table.
TERMS
Score-distribution glossary
- Joint distribution
- The probability assignment across every paired home and away goal count.
- Mode
- The single exact score cell with the highest modeled probability.
- Cumulative mass
- The sum of probabilities for the highest-ranked score cells through a selected rank.
- Clean sheet
- The event that a team concedes zero goals, regardless of its own score.
- Shannon entropy
- A measure in bits of how dispersed probability is across the exact-score outcomes.
- Display cap
- The largest goal count per team included in the reported score square.
EVIDENCE
Retain distribution coverage
Preserve expected-goals sources, data cutoff, display cap, raw included mass, normalized method, ranked score output, and any correction applied outside this page. Report the mode together with its probability and coverage context.
LIMITS
Distribution boundaries
- Goal rates are fixed and home and away counts are independent.
- Entropy depends on the modeled score distribution, not observed competitive quality.
- The page does not include Dixon-Coles low-score correction or dynamic match state.
- Exact-score rankings are sensitive to small changes in expected-goals inputs.
Disclaimer: Use the output for transparent analytical comparison, not as a guarantee or gambling recommendation.
SOURCES
Distribution and football references
FAQ
Questions about exact-score distributions
Why is the most likely score still unlikely?
Probability is divided across many mutually exclusive scores; being first does not mean being probable in absolute terms.
Does higher entropy mean a more exciting match?
No. It means more scoreline uncertainty under this model, not necessarily quality, pace, or entertainment.
Why can both clean-sheet probabilities be high?
When both rates are low, 0-0 contributes to both clean-sheet events.
What display coverage is enough?
Use a documented reporting threshold. For most communication, coverage near 99% avoids hiding meaningful tail scores.
Are score cells independent of one another?
They are mutually exclusive outcomes. The underlying home and away count variables are assumed independent.
Why use a different page from 1X2 probability?
1X2 aggregation answers who wins; this page answers how concentrated or dispersed the full scoreline space is.